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Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a . b = 0 (mod 6), then a = 0 (mod 6) or b = 0 (mod 6). (b) For all integers a and b, if a b = 0 b = 0 (mod 8). (c) For all integers a and b, if a b = 1 (mod 6). (mod 8), then a = 0 (mod 8) or b = 1 (mod 6), then a = 1 (mod 6) or

Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a . b = 0 (mod 6), then a = 0 (mod 6) or b = 0 (mod 6). (b) For all integers a and b, if a b = 0 b = 0 (mod 8). (c) For all integers a and b, if a b = 1 (mod 6). (mod 8), then a = 0 (mod 8) or b = 1 (mod 6), then a = 1 (mod 6) or

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a . b = 0 b = 0 (mod 6). (b) For all integers a and b, if a b = 0 b = 0 (mod 8). (mod 6), then a = 0 (mod 6) or (mod 8), then a = 0 (mod 8) or (c) For all integers a and b, if a b = 1 (mod 6), then a = 1 (mod 6) or b = 1 (mod 6). (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).
Transcribed Image Text:Are the following statements true or false? Either prove the statement is true or provide a counterexample to show it is false. (a) For all integers a and b, if a . b = 0 b = 0 (mod 6). (b) For all integers a and b, if a b = 0 b = 0 (mod 8). (mod 6), then a = 0 (mod 6) or (mod 8), then a = 0 (mod 8) or (c) For all integers a and b, if a b = 1 (mod 6), then a = 1 (mod 6) or b = 1 (mod 6). (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).
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